A general and direct method for the analysis of branched systems is presented, in which transfer matrices are used in Holzer-type solutions. The method is shown here for torsional vibrations, but should be applicable to other branched systems. As presented here, this method is much different than the usual procedure found in the literature. Unlike other methods, no matrix inversions (or equivalent operations) are required to account for branches at a junction. A single determinant giving natural frequencies is arrived at irrespective of the number of branches and junctions. Thus the method is straightforward, compact, and economical for computer solutions.

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